Simplify; express your answer in exponential form. Assume $a\neq 0, k\neq 0$. $\dfrac{{a^{4}k}}{{a^{2}k^{-3}}}$
To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${a^{4}k = a^{4}k}$ On the left, we have ${a^{4}}$ to the exponent ${1}$ . Now ${4 \times 1 = 4}$ , so ${a^{4} = a^{4}}$ Apply the ideas above to simplify the equation. $\dfrac{{a^{4}k}}{{a^{2}k^{-3}}} = \dfrac{{a^{4}k}}{{a^{2}k^{-3}}}$ Break up the equation by variable and simplify. $\dfrac{{a^{4}k}}{{a^{2}k^{-3}}} = \dfrac{{a^{4}}}{{a^{2}}} \cdot \dfrac{{k}}{{k^{-3}}} = a^{{4} - {2}} \cdot k^{{1} - {(-3)}} = a^{2}k^{4}$